Master's Degrees completed - 2012

In this study we investigate the thermal behaviour of an assembly of consecutive cylinders in a counter-rotating configuration cooled by natural convection with the objective of maximizing the heat transfer density rate (heat transfer rate per unit volume). A numerical model was used to solve the governing equations that describe the temperature and flow fields and an optimisation algorithm was used to find the optimal structure for flow configurations with two or more degrees of freedom. The geometric structure of the consecutive cylinders was optimized for each flow regime (Rayleigh number) and cylinder rotation speed for one and two degrees of freedom. Smaller cylinders were placed at the entrance to the assembly, in the wedge-shaped flow regions occupied by fluid that had not yet been used for heat transfer, to create additional length scales to the flow configuration.

It was found that the optimized spacing decreases and the heat transfer density rate increases as the Rayleigh number increases, for the optimized structure. It was also found that the optimized spacing decreases and the maximum heat transfer density rate increases, as the cylinder rotation speed was increased for the single scale configuration at each Rayleigh number. Results further showed that there was an increase in the heat transfer density rate of the rotating cylinders over stationary cylinders for a single scale configuration.

For a multi scale configuration it was found that there was almost no effect of cylinder rotation on the maximum heat transfer density rate, when compared to stationary cylinders, at each Rayleigh number; with the exception of high cylinder rotation speeds, which serve to suppress the heat transfer density rate. It was, however, found that the optimized spacing decreases as the cylinder rotation speed was increased at each Rayleigh number. Results further showed that the maximum heat transfer density rate for a multi scale configuration (with stationary cylinders) was higher than a single scale configuration (with rotating cylinders) with an exception at very low Rayleigh numbers.

Due to constraints and changes in operating conditions, heat exchangers are often forced to operate under conditions of transitional flow. However, the heat transfer and flow behaviour in this regime is relatively unknown. By describing the transitional characteristics it would be possible to design heat exchangers to operate under these conditions and improve the efficiency of the system.

The purpose of this study was to experimentally measure the heat transfer and pressure drop characteristics of smooth tubes at a constant heat flux in the transitional flow regime. The measurements were used to describe the flow behaviour of this regime and attempt to develop a correlation that can be used in the design of a heat exchanger.

An experimental set-up was developed, consisting of an overall set-up, a removable test section as well as a controller, which ensured a uniform heat flux boundary. The test section allowed for the measurement of the temperature along the length of the test section, the pressure drop across the test section, the heat flux input and the flow rate. The measurements were used to determine the heat transfer coefficients and friction factor of the system.

Three test sections were developed with outer diameters of 6, 8 and 10 mm in order to investigate the influence of heat exchanger size. Each test section was subject to four different heat flux cases of approximately 1 500, 3 000, 4 500 and 6 000 W/m2. The experiments covered a Reynolds number range of 450 to 10 300, a Prandtl number range of 4 to 7, a Nusselt number range of 2.3 to 67, and a Grashoff number range of 60 to 23 000.

Good comparison was found between the measurements of this experiment and currently available literature. The experiments showed a smooth transition from laminar to turbulent flow with the onset of transition dependent on the heat flux of the system and with further data capturing, a correlation can be found to describe the Nusselt number in the transitional flow regime.

This work details the development of a computational tool that can accurately model strongly-coupled fluid-structure-interaction (FSI) problems, with a particular focus on thin-walled structures undergoing large, geometrically non-linear deformations, which has a major interest in, amongst others, the aerospace and biomedical industries.
The first part of this work investigates improving the efficiency with which a stable and robust in-house code, Elemental, models thin structures undergoing dynamic fluid-induced bending deformations. Variations of the existing finite volume formulation as well as linear and higher-order finite element Formulations are implemented. The governing equations for the solid domain are formulated in a total Lagrangian or undeformed conguration and large geometrically non-linear deformations are accounted for. The set of equations is solved via a single-step Jacobi iterative scheme which is implemented such as to ensure a matrix-free and robust solution. Second-order accurate temporal discretisation is achieved via dual-timestepping, with both consistent and lumped mass matrices and with a Jacobi pseudo-time iteration method employed for solution purposes. The matrix-free approach makes the scheme particularly well-suited for distributed memory parallel hardware architectures. Three key outcomes, not well documented in literature, are highlighted: the issue of shear locking or sensitivity to element aspect ratio, which is a common problem with the linear Q4 finite element formulation when subjected to bending, is evaluated on the finite volume formulations; a rigorous comparison of finite element vs. finite volume methods on geometrically non-linear structures is done; a higher-order finite volume solid mechanics procedure is developed and
evaluated.
The second part of this work is concerned with fluid-structure interaction (FSI) modelling. It considers the implementation and coupling of a higher-order finite element structural solver with the existing finite volume fluid-flow solver in Elemental. To the author’s knowledge, this is the first instance in which a strongly-coupled hybrid finite element–finite volume FSI formulation is developed. The coupling between the fluid and structural components with non-matching nodes is rigorously assessed. A new partitioned fluid-solid interface coupling methodology is also developed, which ensures stable partitioned solution for strongly-coupled problems without any additional computational overhead. The solver is parallelised for distributed memory parallel hardware architectures. The developed technology is successfully validated through rigorous temporal and mesh independent studies of representative two-dimensional strongly-coupled large-displacement FSI test problems for which analytical or benchmark solutions exist.